f-R-R-x-i-j-x-R-i-N-j-0-1-f-x-f-i-1-i-1-j-1-x-1-j-0-x-lt-1-x-x-lt-0-f-9-5-

Question Number 1057 by 123456 last updated on 25/May/15

f : R_{+} \to R

x = i + j

x \in R_{+}

i \in N

j \in [0, 1)

f (x) = {\begin{cases} f (i - 1) + (i + 1) (j + 1) & x ⩾ 1 \\ j & 0 ⩽ x < 1 \\ x & x < 0 \end{cases}

f (9.5) = ?

Answered by prakash jain last updated on 26/May/15

f (9, 5) = f (8) + 10 \cdot 6

= f (7) + 9 + 10.6

= f (6) + 8 + 9 + 10.6

= f (5) + 7 + 8 + 9 + 10 \cdot 6

= f (4) + 6 + 7 + 8 + 9 + 10 \cdot 6

= 1 + 2 + 3 + \dots + 9 + 10 + 10 \cdot 5

= 105